Relational queries computable in polynomial time
Information and Control
Languages that capture complexity classes
SIAM Journal on Computing
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
An extension of fixpoint logic with a symmetry-based choice construct
Information and Computation
Non-deterministic languages to express deterministic transformations
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Theoretical Computer Science
Bisimulation-invariant PTIME and higher-dimensional &mgr;-calculus
Theoretical Computer Science
On a New High Dimensional Weisfeiler-Lehman Algorithm
Journal of Algebraic Combinatorics: An International Journal
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Universality of data retrieval languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Definability and Descriptive Complexity on Databases of Bounded Tree-Width
ICDT '99 Proceedings of the 7th International Conference on Database Theory
A Restricted Second Order Logic for Finite Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
The Quest for a Logic Capturing PTIME
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Choiceless Polynomial Time, Counting and the Cai--Fürer--Immerman Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
Planar graphs: logical complexity and parallel isomorphism tests
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
From invariants to canonization in parallel
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Fixed-Point Definability and Polynomial Time on Graphs with Excluded Minors
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Capturing Polynomial Time on Interval Graphs
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Testing graph isomorphism in parallel by playing a game
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Set graphs. I. Hereditarily finite sets and extensional acyclic orientations
Discrete Applied Mathematics
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The question of whether there is a logic that captures polynomial time was formulated by Yuri Gurevich in 1988. It is still wide open and regarded as one of the main open problems in finite model theory and database theory. Partial results have been obtained for specific classes of structures. In particular, it is known that fixed-point logic with counting captures polynomial time on all classes of graphs with excluded minors. The introductory part of this paper is a short survey of the state-of-the-art in the quest for a logic capturing polynomial time. The main part of the paper is concerned with classes of graphs defined by excluding induced subgraphs. Two of the most fundamental such classes are the class of chordal graphs and the class of line graphs. We prove that capturing polynomial time on either of these classes is as hard as capturing it on the class of all graphs. In particular, this implies that fixed-point logic with counting does not capture polynomial time on these classes. Then we prove that fixed-point logic with counting does capture polynomial time on the class of all graphs that are both chordal and line graphs.